On Nonlinear Regularized Traces of Second-Order Differential Operators on a Star Graph
Fazullin Z.Y. Kanguzhin B.E. Satpaeva Z.Z.
July 2025Pleiades Publishing
Lobachevskii Journal of Mathematics
2025#46Issue 73110 - 3114 pp.
Abstract: In 2000, A.M. Savchuk and A.A. Shkalikov showed that the regularized trace of the Sturm–Liouville operator with a potential in the form of a distribution is a nonlinear functional of the potential. It turned out that the linearity or nonlinearity of the regularized traces of the Sturm–Liouville operator depends on the type of boundary conditions. In the Dirichlet case, the regularized trace is a nonlinear functional, and in the case of periodic boundary conditions, the nonlinearity of the regularized trace is violated. In this paper, we show that the regularized traces of the Sturm–Liouville operator, both in the case of Robin conditions and in the case of an analogue of periodic conditions on a star graph, are nonlinear functionals of the initial data of the operator.
boundary conditions , matching conditions , star graph , stiffness coefficient , Sturm–Liouville operator
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Institute of Informatics, Mathematics and Robotics, Ufa, 450069, Russian Federation
Ufa University of Science and Technology, Ufa, 450069, Russian Federation
Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, 050040, Kazakhstan
Sarsen Amanzholov East Kazakhstan University, Ust-Kamenogorsk, 070004, Kazakhstan
Institute of Informatics
Ufa University of Science and Technology
Al-Farabi Kazakh National University
Institute of Mathematics and Mathematical Modeling
Sarsen Amanzholov East Kazakhstan University
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